Solved – How to obtain covariance matrix for constrained regression fit

Is there an easy way to obtain the covariance of the parameters from a constrained regression fit?

I am using the PCLS function in the MGCV package in R to fit the constrained regression, however I am open to other approaches.
The constraint I am imposing is that the coefficients must be positive.

At first I would go with very simple bootstrap.

Basically something as follows:

  1. Create a new data-set by resampling pairs of $(x,y)$.
  2. Run your regression on this new data set and you will get some parameters $hat beta$.
  3. Repeat 1 and 2 as many times as possible. Now you will have a large sets of $ hat beta$
  4. Now just take the sample covariance of your $hat beta$.
  5. Done

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